This paper presents a new algorithm of path planning for mobile robots, which utilises the characteristics of the obstacle border and fuzzy logical reasoning. The environment topology or working space is described by the time-variable grid method that can be further described by the moving obstacles and the variation of path safety. Based on the algorithm, a new path planning approach for mobile robots in an unknown environment has been developed. The path planning approach can let a mobile robot find a safe path from the current position to the goal based on a sensor system. The two types of machine learning: advancing learning and exploitation learning or trial learning are explored, and both are applied to the learning of mobile robot path planning algorithm. Comparison with A* path planning approach and various simulation results are given to demonstrate the efficiency of the algorithm. This path planning approach can also be applied to computer games.